Risk-Based Inspection and Strength Evaluation of Suspension Bridge Main Cable Systems (2023)

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35 C H A P T E R 3 Review of NCHRP 534 Approach Introduction Since its publication in 2004, NCHRP NCHRP Report 534 “Guidelines for Inspection and Strength Evaluation of Suspension Bridge Parallel Wire Cables” (herein referred to as NCHRP Report 534), has provided a standardized method for use by owners and investigators to inspect and evaluate main cables and has been applied on suspension bridges worldwide. The research behind the development of this approach was performed under NCHRP Project 10-57 and is contained in a final report entitled “Structural Safety Evaluation of Suspension Bridge Parallel Wire Cables” (herein referred to as Project 10-57), also published in 2004. A supplemental report based on NCHRP Report 534 was released by FHWA in 2012 called the “Primer for the Inspection and Strength Evaluation of Suspension Bridge Cables”. NCHRP Report 534 contains very detailed methods and procedures, which are necessary to ensure consistent and repeatable results. Although they may appear daunting to investigators at first glance, the guidelines are organized into sections to make the information more manageable. These sections are arranged to follow the typical sequence of a main cable investigation. The sections below follow the same organization as NCHRP Report 534 and are intended to provide a thorough explanation of the inspection procedures and methodology used during an actual main cable inspection. Highlighting the important details of the current approach in NCHRP Report 534 will facilitate the discussion of proposed changes which are dealt with in subsequent sections of this report. General Prior to selecting locations for the internal inspection of the main cable, an external inspection of the cables is performed to identify any defects or deficiencies (as discussed in Article 2.2.3 of NCHRP Report 534). The external inspection may be done routinely as part of the biennial inspection of the bridge or performed specifically for the purpose of the internal investigation. If previous internal inspections of the cable have been performed, that information can also be used to select locations for subsequent inspections. For example, particular attention would be given to panels where a high number of broken wires or a high percentage of wires with Stage 4 corrosion had been observed. Locations for internal inspection may also be selected based on their location along the cable. Historically, the worst cable deterioration has been observed near the quarter-points of the cable, though damage has also been observed near low points (where water tends to collect). A typical internal inspection consists of the following steps: • Installation of access scaffolding, • Removal and disposal of wrapping wire,

36 • Wedging and preparing the cable for inspection, • Recording the stage of corrosion of all exposed wires, • Recording the location of any broken wires, along with the gap distance between the wire ends (where possible), • Removal of sample wires for testing, and recording the gap distance between cut ends, • Repair of broken wires (if applicable) and those cut for test samples by splicing in new wires, • Removal of wedges (when a corrosion inhibiting oil is applied to the interior of the cable, the lower wedges are removed first, then the oil is applied, followed by removal of the remaining wedges), • Re-compaction of the cable, • Application of a corrosion inhibiting compound to the surface of the cable (typically a zinc oxide paste), • Rewrapping the cable with galvanized wire and replacement of caulking at cable bands, • Cleaning the wrapping and painting the surface of the cable. In a typical cable investigation, eight panels are selected (four per cable) for internal inspection. Each panel is wedged at eight locations around the perimeter and inspected full length between the cable bands. It should be noted that the four locations per cable chosen typically constitutes less than 3% of the total cable length. Furthermore, the field inspection of all wires within the eight wedge lines allows for direct observation of approximately 10% of the total wires in the cross-section of the cable. When calculating the strength of the main cable, it is important to remember that only a small portion of the wires in the cable are actually inspected and sampled. Because of this relatively small sampling, there is a high probability that the worst panel location will not be found on the first inspection of the cable. The calculated safety factor is therefore established with a certain confidence level and must be evaluated against the possibility that a lower safety factor may exist elsewhere along the cable. Article C6.4 of NCHRP Report 534 recommends that immediate remedial action be taken whenever the safety factor is found to be less than 2.15. Inspection The internal inspection is performed by first installing temporary work platforms at each panel location. The platforms are typically suspended from the main cable by attaching them to the cable bands. The temporary platforms are typically designed by the contractor’s engineer per the design criteria provided in the design plans. The platforms must be of sufficient length to allow inspection of the full panel length. Class 3P containment is typically provided during unwrapping and wedging operations in order to collect construction debris (often containing lead waste) and prevent such materials from dropping onto traffic below. Construction workers are required to follow lead protection procedures in accordance with the project’s Health and Safety Plan. This typically requires the use of protective coveralls during performance of the work along with respirators for operations that involve the release of airborne debris (i.e. unwrapping, wedging and cleaning the cable). For inspectors, lead exposure tends to be more limited since the cable is not being disturbed during the inspection work. The use of coveralls, gloves and eye protection is typically sufficient, however additional measures may be stipulated based on the bridge owner and/or applicable governmental requirements. The wrapping wire is then removed and the surface of the cable is cleaned of all loose materials, such as existing red lead paste, existing zinc oxide paste, grease, rust, etc. Plastic wedges are then driven into the cables with sledgehammers. The wedging pattern typically consists of eight radial wedge lines

37 at the 12:00, 1:30, 3:00, 4:30, 6:00, 7:30, 9:00, and 10:30 positions (clock positions are referenced to a standardized direction along the cable, i.e. “looking upslope”), as shown in Figure 21. Figure 21. Cable Wedge Pattern Wedges are driven to the center of the cable starting at the center of the panel and extending to within approximately 3 feet from the cable band at each end of the panel. The contractor drives one wedge line at a time using stacks of two wedges along the length of each wedge line, to allow for proper inspection access by the engineer. Contractors typically prefer to drive all eight wedge lines at once, as it increases their productivity, but this should only be allowed if it is acceptable to the engineer (as it causes an increase in tension in the wires and limits the opening width of the wedge line). Classifying Corrosion Stage of Wire Once the cable is opened, the condition of each of the exposed wires is classified based on the stages shown in Figure 22, adopted from the research performed by Hopwood and Havens in 1984 (from Figure 1.4.2.2-1 and as defined in Article 1.4.2.2 of NCHRP Report 534): Source: Mayrbaurl and Camo (2004b) Figure 22. Wire Corrosion Stages

38 Stage 1: Spots of zinc oxidation on the wires (like-new condition); Stage 2: Zinc oxidation over the entire wire surface (no ferrous rust); Stage 3: Spots of brown rust covering up to 30% of the surface of a 3-in. to 6-in. length of wire; Stage 4: Brown rust covering more than 30% of the surface of a 3-in. to 6-in. length of wire. In some cases, it is necessary to establish an additional stage of wire classification to account for special field conditions. For example, a Stage “2B” designation could be assigned to wires with “black” areas exhibiting depletion of zinc coating since it would not be known if these wires would be Stage 2 or Stage 3 until they are tested (per Article C2.4.3.1 of NCHRP Report 534). That is, the depletion of galvanizing can indicate the end of Stage 2 or the beginning of Stage 3. The stage of each of the observed wires within the wedge line is recorded at three locations along the opened length in accordance with Article 2.4.3.1 of NCHRP Report 534. Wire conditions are recorded using a form developed from Figure 2.3.1.2.4-2 of NCHRP Report 534 (customized for the number of wires in the main cable of that particular bridge). Although wire conditions are variable along the length of the panel, only the highest corrosion stage within each section is recorded on the form. The final rating of each wire, which is used in the analysis of the cable capacity, is based on the highest corrosion stage found within the panel. This is due to the weakest link effect whereby the strength of each wire is controlled by the worst condition anywhere along its length. The field condition notes from each panel are combined to form composite corrosion maps for each panel (as described later in Article 2.1.2.4.1). Broken Wires After the wires have been inspected, all wedges (except those closest to the cable bands) are removed in order to provide some slack in the wires and make it easier to search for loose or broken wires (for panel lengths in excess of 25 ft., it may be necessary to leave some intermediate wedges in place). A probe is used to “pluck” the wires to help detect for any with low tension. Due to the inherent cast, or curvature, of a de-tensioned wire, broken wires will tend to curl to the surface if the adjacent wires are disturbed in this manner. Any broken wires found within the wedge lines or on the exterior of the cable are recorded using the form from Figure 2.3.1.2.4-3 of NCHRP Report 534. Note that the count of observed broken wires should include loose wires (those with low tension) that may be encountered during inspection (indicating the presence of a wire break in an adjacent panel). Accessible broken wires (usually limited to the top 10 rows from the surface) are usually repaired by splicing a length of new galvanized steel wire (No. 6 gauge, 0.196 in. diameter with Class A zinc coating) between the broken ends using swaged ferrules. Deeper wires are not typically repaired since the wedge opening becomes too narrow for the swaging equipment. Wire ends are tensioned using a come-along fitted with special wire grips. Repair wires are tensioned to a value calculated to be within 10% of the dead load force (in accordance with Appendix D of NCHRP Report 534). A higher initial tension force is typically applied (approximately double the required final force) in order to achieve the desired final tension after expected losses. Sample Wires Samples for laboratory testing are cut from unbroken wires and then repaired in a similar fashion as broken wires. The number of sample wires is determined from Table 2.4.3.5.1-1 of NCHRP 534. Note that the number of samples shown in NCHRP Report 534 is based on an assumed value for the percentage of cracked wires (5% for Stage 3 and 64% for Stage 4). For most bridges, this results in an overly conservative estimate of the required samples. However, since the actual percentage of cracked

39 wires is not typically known prior to the investigation (unless the cable has been evaluated previously), it is appropriate to err on the conservative side. Wire sampling is usually limited to the outer 10 rings of the cable because deeper wires would not accommodate splicing and therefore would not be repairable. Not all wires within the cable cross- section remain parallel, as such, a specific wire may not necessarily remain in the same ring along the length of the panel. Therefore, a reference point a set distance from one of the cable band may be used to define the ring number of the wire. When the sample wires are cut, the gap distance between the two ends of the wire is recorded by measuring to marks scribed on adjacent wires. This data is used to estimate the capacity of the cable bands to redevelop the force in a broken wire due to the friction that develops between adjacent wires. Before the sample wire are removed, they are tagged to designate the cable, panel number, wedge line and wedge line side and the ring number (at the reference point). An appropriate location should be selected in advance for the contractor to store the sample wires. The storage area must be secure, dry, preferably on site, and capable of accommodating the anticipated number of samples. Care must be exercised by the contractor in handling sample wires to avoid damaging the identification tags. Sample wires are cut to different lengths and different locations within a given wedge line in order to offset the locations of ferrules when wire splices are completed. This results in sample wire of different lengths. The ferrules used for splicing the wires are staggered a minimum of 1’-6” measured along the length of the cable. All broken and sample wires are shown on the composite corrosion maps for each panel. Inspection Completed Once the inspection is completed, the wedges may be removed (if desired, the cable may be treated with corrosion inhibitor by pouring it into the top wedge lines; the bottom few wedges are removed to help contain the oil within the interior of the cable). The cable is then re-compacted to its original diameter (or as close as possible) using a custom-made hydraulic compacting machine. In certain cases, it may not be possible to re-compact the cable to within the specified tolerance of its original diameter (+/- 5%), particularly at locations where wire splices are located at or close to the surface of the cable. During the re-compacting process, temporary strap bands are applied at a 24 in. spacing to keep the cable tightly compacted as the machine moves up the cable. A coat of zinc oxide paste is applied to the cable exterior in stages just prior to wrapping (red lead, which was often used during the original construction of the cable, is no longer used due to worker health concerns). The cable is then re- wrapped with No. 9 gauge, 0.148 in. diameter steel wire with a Class A zinc coating under a minimum tension of 300 lbs using a wrapping machine (which must often be custom made to fit the specific diameter main cable). The temporary strap bands are removed individually as the wrapping machine approaches each one in order to hold the cable in its compacted state. Finally, the cable is painted using the bridge owner’s preferred coating system (often an elastomeric paint is used to accommodate the flexibility of the cable). Skid resistant granules are often broadcast into the intermediate coat of paint to improve grip for inspectors and maintenance personnel. Finally, cable band gaps are sealed with caulk to prevent water intrusion. It is important to provide a gap in the caulk on the downhill side of the cable band to act as a drain opening for any water that becomes trapped within the cable (no matter how much care is taken during construction, water will always be present due to humidity, etc.).

40 A detailed summary of all construction activities performed as part of the cable investigation, including the dates on which they were performed should be documented by the construction inspection team for future reference. Laboratory Testing Sample wires extracted from the main cable are delivered to a laboratory for testing. There they are cut into shorter lengths, called wire specimens, which are then subjected to tensile testing. The wire specimens are typically cut to 18 inches in length which leaves approximately 12 inches between the grips of the testing machine. The test results from the standard length specimens are used to determine the wire properties required for calculating the strength of the cable. Tensile Tests Enhanced tensile tests, in which the full range of stress and strain is recorded to failure, are performed in accordance with ASTM A370 and E8 using the extension under load method to determine the following: • breaking load • yield strength • tensile strength • elongation • reduction of area • modulus of elasticity Testing is typically performed using a computer controlled universal testing machine fitted with hydraulic wedge grips (50 kip capacity). Force and displacement data are collected while the specimens are loaded at a constant displacement rate to failure. Stresses are calculated based on the nominal ungalvanized wire diameter of 0.192 inch. Strain is measured using a pair of linear displacement sensors with a 10 inch gage length (standard specimens are 12 inches long between grips). The properties of the individual specimens are then used to determine the minimum ultimate wire strength/strain over one panel according to the equations in NCHRP Report 534. A test report should be provided by the laboratory which includes the full stress-strain curve for each specimen with the measured ultimate strength, ultimate elongation (as measured along a gage length), Young’s Modulus, and yield strength. The test report should also include a summary table which, in addition to the tensile test data indicated above, contains the following information about the fracture morphology of each test specimen: • Corrosion stage of wire specimen (as provided from field inspection and verified in the lab) – Stage 1, 2, 3 or 4 • Does fracture surface indicate there was a pre-existing crack? – Yes/No • Description of fracture surface – A: ductile – cup and cone – B: ductile – cup and cone with shear lips above and below fracture plane – C: brittle – ragged with no reduction of area – D: brittle with crack – transverse fracture with pre-existing crack • Location of fracture – Top or bottom grip – Within gage

41 Oftentimes, wires will break outside the 10” gage length (this is typical of main cable wires due to the residual stress caused by the “cast” of the wire resulting from the fabrication process). Strains beyond the ultimate stress are therefore not recorded, which results in a slight underestimate of the ultimate strain. The tensile tests are also used to determine the number of specimens with pre-existing cracks. Uncracked wires fail in a ductile manner, achieving strains of about 4%. Their failure surface shows a reduction in the wire diameter at the failure location (necking) along with a “cup and cone” failure surface. In contrast, wires with pitting or cracking tend to fail in a brittle manner at relatively low strains (less than about 2%) and exhibit a ragged failure surface. The number of specimens cut from each wire varies as a result of sample wire length but also due to the variability of the corrosion stage present on the sample wire. Ideally, only those specimen’s representative of the highest corrosion stage of the sample wire are tested. The effect of testing all specimens is a potential reduction in statistical error, yet it can also introduce additional variability if the specimens are not of the same corrosion stage (which has the net effect of decreasing the computed strength of the sample wire). Testing of non-standard length specimens has been used by some in the past in order to determine the presence of pre-existing service cracks (longer sample lengths are used to increase the likelihood of detecting cracks). The tensile testing of long (72 inch long) specimens may be performed for the purpose of detecting cracks. The tensile strength data from these tests should not be used to determine the wire properties for the cable strength calculations. Results of previous studies using long, non-standard test specimens indicate that the ultimate load decreases over that of standard (18 inch long) specimens. The procedure for tensile testing of long specimens is identical to that of the standard specimens, except that strain is only measured up to 2% to avoid risk of damaging the extensometer at failure. Following the test, the fractured ends of suspect wires are visually examined under a stereoscopic microscope to determine if the failure occurred at a pre-existing crack. Although the use of long specimens to identify cracks is not a test method that is explicitly recommended in NCHRP Report 534, results from previous inspections show that this can be a valuable method to accurately identify pre-existing cracks and underscores the importance of evaluating the full length of all sample wires. Fractographic Examination of Suspect Wires Cracked wires are those with pre-existing service cracks (they exist prior to testing). Typically, these cracks are too minute to detect except by examination of the fracture surface generated by tensile testing. When wire specimens undergo tensile testing, any cracked wires will fail at the location of the pre-existing crack. The fracture surface of a cracked wire has unique characteristics that distinguish it from an uncracked wire - this study of the fracture surfaces of materials is known as fractography. The techniques associated with the fractographic evaluation of wires are outlined in Articles 3.2.4 and 3.2.5 of NCHRP Report 534. For the purpose of detecting cracked wires, the fractographic evaluation typically consists of a visual examination of the fractured ends of the test specimen under a low power (approximately 20X magnification) stereoscopic microscope. NCHRP Report 534 also recommends that the crack depth be measured.

42 The primary purpose of the fractographic evaluation is to evaluate the wire specimen fracture surfaces generated by tensile testing for wires with pre-existing cracks. All specimens are visually examined under a stereoscopic microscope in accordance with FHWA Guidelines for “Inspection of Fracture Critical Bridge Members” of Cable Suspension Bridges (FHWA-1P-86-26). Any wires identified as having pre-existing cracks are selected for further fractographic study, consisting of Scanning Electron Microscopy (SEM). The detailed study looks for signature signs of pre-existing cracks, namely, they initiate from pitting on the outer surface of the wire, then progress transversely (often exhibiting a stepped profile) with little plastic deformation, as is characteristic of stress corrosion cracking. Using the results of the fractographic evaluation of the specimens, the number of cracked sample wires is calculated and presented along with the group wire properties. Note that the percentage of Stage 3 wires considered cracked for calculation purposes is determined by taking the actual percentage and multiplying by a factor of 0.33, per Articles 4.4.2 of NCHRP Report 534, in order to avoid overestimating the number of cracked Stage 3 wires. Additional Testing Additional testing recommended by NCHRP Report 534 are used to obtain baseline information about the original properties of the wire. Most of these tests do not need to be repeated with subsequent investigations and they test material properties which do not change over time. These tests include: • Chemical composition • Hydrogen embrittlement • Slow strain rate testing • Stress corrosion testing • Ductility testing • Weight of coating tests • Preece test Evaluation of Field and Laboratory Data Once the cable has been inspected and laboratory testing completed, cable strength is calculated for each location in accordance with the referenced Articles of NCHRP Report 534, as follows: • The total number of wires at each stage of corrosion is estimated per Article 4.3.2, • The total number of broken wires is estimated per Article 4.3.3, • Wires were sorted into groups and the number of cracked wires is estimated per Articles 4.4.1 and 4.4.2, • The properties of the wires composing each group are calculated in accordance with Articles 4.4.4, • The wire redevelopment length is calculated per Articles 4.5.2, • The cable capacity is then calculated using one of the three models described below and presented in Chapter 5. Number of Wires per Corrosion Stage The method for estimating the number of wires in each corrosion stage is outlined in Article 4.3.2 of NCHRP Report 534. The first step in this method involves assigning a corrosion stage to each wire within the wedge line based on the highest observed corrosion stage of that wire from the inspection of

43 multiple segments along the panel. Note that this procedure assumes that wires remain parallel (the wire stays in the same ring) over the length of the panel. Since this is not always the case, it can result in somewhat conservative results in that a higher rating may be assigned to a different wire. Once this corrosion stage is assigned, it is then applied to all other wires in that ring within the half-sector containing the rated wire. A spreadsheet is typically used to help automate the calculations for determining the number of wires in each stage, following the format shown in Figure 4.3.2-1 of NCHRP Report 534. Broken Wires The method for estimating the total number of broken wires is outlined in Article 4.3.3 of NCHRP Report 534. This method involves calculating the total number of broken wires based on the number and location of the observed broken wires. That is, whenever broken wires are found on the outer surface as well as the interior of the wedge lines, the total number of broken wires will be greater than the observed number of broken wires. A spreadsheet is typically used to help automate the calculations for determining the number of wires, following the format shown in Figure 4.3.3.1-1 of NCHRP Report 534. There are two different counting methods that can be used, depending on where the observed broken wires are located. The first method is used when broken wires are found within the interior of the cable beyond the first few rings from the surface. A second method is used if broken wires are found only at or near the outside ring. If both conditions are found, then a combination of the two counting methods is implemented. The location of broken wires is also shown graphically on the corrosion maps. Broken wires found on the interior of the cable are given greater weight than surface wires in estimating the total number of broken wires. That is, finding just a few wires deep in the cable results in a substantial increase in the estimated number of broken wires. This is because broken wires located on the outside surface of the cable (Ring 1) have a high probability of being observed during inspection (the wire cast causes them to project out of the cable), while interior wires have a lower probability of detection because the surrounding wires tend to hold them in place; and the deeper they are inside, the less likely they are to be observed. Therefore, when a broken wire is found within the cable, it is likely that wire represents only a fraction of the total number of broken wires. Wire Properties The wires are divided into the following groups for calculating cable strength: Group 1: samples exhibiting Stage 1 corrosion* Group 2: samples exhibiting Stage 1 and/or Stage 2 corrosion, Group 3: samples exhibiting Stage 3 corrosion that are not cracked, Group 4: samples exhibiting Stage 4 corrosion that are not cracked, Group 5: samples exhibiting Stage 3 and 4 corrosion that are cracked. *Typically, the properties of Stage 1 and Stage 2 wires are similar enough that both are designated as Group 2 wires, to simplify the calculations. Broken wires are effectively treated as Stage 4 for the purpose of calculating cable strength, as per Article 5.3.2.3 of NCHRP Report 534. All cracked wires are subtracted from the group assigned by their corrosion stage and added together to form Group 5.

44 Assigning Sample Wires to Groups For bridges where it is observed that the corrosion stage varies along the length of the wire, it is important to categorize the wire corrosion stage on the basis of an inspection of the individual specimens after they are cut from the wire. In some cases, the corrosion stage determined in this manner may result in assigning a higher corrosion stage to a wire than had been assigned in the field. This is due to the fact that a more thorough inspection can be performed after the sample wire has been removed from the cable. The following procedure may be used for assigning corrosion stage for wire grouping purposes when wire corrosion is highly variable along the length: • The standard length (18-inch long) specimens are individually rated for corrosion stage (corrosion stage for long specimens is not considered for grouping of standard specimens); • The corrosion stage for the wire is based on the specimen with the worst (highest) corrosion stage (this stage takes precedent over the field determined value if they are different); • The sample wire is assigned a wire group based on this stage and the test data from all specimens from that wire are used to determine the properties of the sample wire. For example, if a sample wire was classified as Stage 3 in the field, but the subsequent inspection of the individual specimens from that wire finds one or more that are Stage 4, the entire sample wire will be considered to be a Stage 4 wire. Furthermore, if this particular sample wire was cut into four specimens and upon examining the corrosion stages of the specimens it is determined that two specimens are Stage 4 and 2 specimens are Stage 3, the entire sample wire and all wire specimens from that wire will be assigned to Group 4 (assuming it is uncracked). The test results from all four specimens will be used to determine the properties of the sample wire. It is believed that this procedure is in keeping with the intent and language of NCHRP Report 534, as follows: • Article 2.4.3.1: “Each wire is then reassigned the highest observed corrosion stage found on that wire in the opening length, after comparing the recorded data for the wire in each segment”. • Article C2.4.3.1: “Only the highest stage found along the length of the wire is used in the analysis of cable capacity”. • Article C2.4.3.5.3: “When the corrosion stage varies along the length of the sample wire, the specimens to be tested for strength should be cut from the worst areas of the wire”. • Article 3.2.1: “Before sample wires are cut into specimens of suitable length for testing, they should be inspected and assigned to the appropriate corrosion stage”. • Article 3.2.1: “All of the specimens from a given sample should be at the same stage of corrosion, but it is understood that this is not always possible.” Where this procedure differs from NCHRP Report 534 is in the fact that all specimens were tested, not just those that represented the rated corrosion stage of the wire. Under normal conditions when performing testing in accordance with NCHRP Report 534, the Stage 3 specimens from a Stage 4 sample wire would simply not be tested (or the test data would not be used). However, it is believed that the wire group properties determined from testing all specimens from a wire will not differ significantly from those determined by only testing representative sections. NCHRP has a formula for determining the minimum strength of a wire based on the results of multiple specimens from that wire (Equation 4.4.3.2-1) – this is the “weakest link” effect. Thus, the use of multiple specimens from a single wire is inherent in the NCHRP formulation. Furthermore, inspection of the tensile test results indicated that the data for all specimens from a wire tended to be similar, regardless of their rated corrosion stage (except for Group 5 cracked specimens). This is not to say that corrosion rating is irrelevant, only that the strength of a wire is dependent more on which wire is tested rather than which portion of the wire is tested.

45 The bottom line is that it is not necessary to test all sections along a sample wire to determine the properties of the wire. NCHRP Report 534 recognizes that visual corrosion rating allows one to minimize the number of tests while obtaining sufficiently accurate results. Additional testing, while not required, does not appear to significantly alter the results. Cracked Wires The percentage of cracked wires for each corrosion stage is determined directly from test results. The number of cracked wires in the cable is then a function of the percentage of Stage 3 and 4 wires (primarily Stage 4) within the cross-section, as well as the effective development length, due to the potential for cracked wires to occur in adjacent panels. Per Article 3.2.5 of NCHRP Report 534, a sample wire is considered cracked if any of the specimens cut from that wire are found to contain a pre-existing crack. Per Article 4.4.2 of NCHRP Report 534, the percentage of cracked Stage 4 wires in the cable is assumed equal to the percentage of cracked Stage 4 samples; whereas the percentage of cracked Stage 3 wires is assumed to be 0.33 times the number of cracked Stage 3 samples. According to Article C4.4.2 of NCHRP Report 534, the 0.33 factor is used to account for the fact that, unlike Stage 4 wires which are typically near the surface of the cable and therefore easily accessible for taking samples, Stage 3 wires are generally found deeper in the cable. However, samples of Stage 3 wires are usually taken from the outer region of the cable with Stage 4 wires nearby, where the wires are more likely to be cracked. Thus, without the 0.33 factor, the number of cracked Stage 3 wires in the cable would be overestimated. Properties of Wire Groups After the wire specimens have been tested, it is necessary to determine the minimum properties of the various groups for use in the strength calculations. Due to the weakest link effect, the cable is only as strong as the weakest point along its length, taken to be equal to a panel length (a unique value for each bridge). Since the specimen length is much shorter (typically about 12 inches, measured between the jaws of the test machine), it is necessary to adjust the direct test results to determine the minimum properties over the much larger panel length. This involves a statistical procedure that is outlined in Article 4.4.3.2 of NCHRP Report 534. Wire stresses have been calculated using the nominal wire diameter of 0.192 inches. It should be noted that the actual wire diameter, including galvanizing, is typically used when reporting wire strength in wire specification (original construction as well as the current ASTM A586 specification). Using the smaller diameter results in a higher wire strength when compared to the specification value (by approximately 4%, which is the ratio of the diameters squared). For example, a wire with a strength of 215 ksi based on the gross metallic area (including galvanizing) is equivalent to having a strength of 224 ksi based on the nominal diameter. Care needs to be taken when calculating forces to ensure that a consistent diameter has been used for both stress and wire area. It is important to recognize that in some cases the nominal diameter is used, and in other cases the gross metallic area (including galvanizing) is used. The diameter does not affect the cable strength calculations performed herein since they involve only force (the same diameter has been used for all the data). Tests have shown that the galvanized coating does not contribute to the strength of the wire (the breaking strength does not change by removing the galvanized coating). However, galvanized wires do have a slightly lower wire strength compared to bright wires as a result of the high heat associated with the galvanizing process (strength is reduced by approximately 3% for the same diameter). Since the zinc coating does not contribute to strength and the galvanizing is often depleted when dealing with samples of wire extracted

46 from bridges in service, the use of the nominal wire diameter appears to be more appropriate for the purpose of reporting test results. Wire Redevelopment Length Wires that are broken in adjacent panels are redeveloped in the panel under investigation through friction. Once a wire breaks, the force in that wire at the location of the break is zero. However, due to friction developed between the broken wire and those adjacent to it, the force in the wire gradually increases until it is the same as that in the surrounding wires. This friction develops due to the confining force exerted on the cable by both the wrapping wire and the cable bands. For simplicity, NCHRP Report 534 conservatively assumes that all redevelopment occurs at cable band locations, as shown in Figure 23. The number of cable bands required to redevelop a wire is calculated based on the size of the gap between the ends of broken wires or those cut for samples and the service force in the cable, in accordance with Article 4.5 of NCHRP Report 534. This is then used to determine the number of panels required to redevelop the wire to 95% of the mean strength of Group 2 wires on both sides of the break. This is the development length, that is, the number of panels over which a broken wire will affect the strength of the cable at the panel under investigation. For example, the cable shown in Figure 23 requires three cable bands to redevelop the wire, with each band developing 1/3 of the wire force. The resulting development length is five panels. Figure 23. Wire Redevelopment The estimated force in wires broken in adjacent panels consists of two components. The first is the force in wires that are assumed to be broken in other panels over the redevelopment length. Since adjacent panels are not typically included in the inspection, they are assumed to have the same number of broken wires as the inspected panel. The second component is the force redeveloped in cracked wires that break as the stress in the cable is increased to the assumed value. Here again, adjacent panels within the redevelopment length are assumed to contain the same number of cracked wires as the panel being evaluated.

47 Estimation of Cable Strength The properties of the test specimens determined from the tensile tests are used to establish the ultimate strength and strain of the wires composing each group per Article 4.4 of NCHRP Report 534, as follows: 1. The ultimate strength (strain) data of all the specimens composing a sample wire were collected, 2. The mean and standard deviation of their ultimate strengths (strains) were calculated, 3. The probable minimum ultimate strength (strain) of a length of wire equal to the cable band spacing was calculated, 4. This was repeated for all samples of a group and the mean and standard deviation of the probable minimum ultimate strength (strain) was calculated for that group, 5. The mean and standard deviations were then used to determine the Weibull distribution for the ultimate strength (strain) of each group. For all models, the condition of any wire is assumed the same in adjacent panels as in the panel being evaluated. It is also assumed that wires at a given stage in the evaluated panel will break before wires at the same stage or better in adjacent panels. Thus, all uncracked wires are assumed to fail in the panel being evaluated. The three models used to estimate the strength of the cable at the inspected locations are called brittle wire models, as they assume that individual wires fail in a sudden, brittle manner when the stress or strain in the wire reaches a certain level. All unbroken wires are assumed to share equally in carrying the applied load. The following sections describe each of the three models in more detail. The first two models are based on stress, the third on strain. Simplified Strength Model This model is a simplification of the Brittle Wire Model, described below. Cracked and broken wires are assumed not to contribute to the strength of the cable. It is therefore conservative and may underestimate the strength of the cable by up to 20%. Because it neglects broken and cracked wires, it should be used only where their estimated number is no greater than 10% of the total wires in the cable. The Simplified Model also differs from the Brittle Wire Model in that a single Weibull distribution function is used that combines the properties of groups 2, 3 and 4 wires. The use of a single distribution function allows for the derivation of a closed form solution of the cable strength equation (Eq. 2.4-23 of Article 2.6.2.2 of Project 10-57). However, the form of the equation used in NCHRP Report 534 has been simplified by the introduction of a strength reduction factor, K, determined from Figure 5.3.3.1.2-1 of that report. The use of graphical means to determine K helps to minimize computational effort as compared to the closed form solution, though at the expense of a slight loss of precision. Brittle Wire Model The Brittle Wire Model assumes that all the wires have the same stress-strain curve, thus, all the wires will have the same stress and carry equal portions of the applied load. A wire is assumed to fail immediately upon reaching its ultimate stress, at which time its share of the force is transferred equally to the remaining wires. In reality, the uncracked wires will deform plastically prior to fracture, allowing further development of the cable strength, making this model somewhat conservative. The cable strength is calculated by first assuming a stress in the cable. The number of broken wires in each group is calculated using the cumulative Weibull distribution function of the tensile strength

48 for that group. The assumed stress is then multiplied by the area of the remaining wires and estimates of the force in wires broken in other panels and redeveloped in the panel under consideration are added to determine the total force in the cable. The assumed stress is then varied until the maximum cable force is found. This is the estimated cable capacity. A spreadsheet can be used to automate this process (e.g. Microsoft Excel’s “Solver” add-on). Limited Ductility Model The Limited Ductility Model assumes that a wire fails upon reaching its ultimate strain. The general form of this model accounts for individual differences in the stress-strain curves of the specimens tested and must be used whenever there is appreciable variability in the experimental data. The special case of this model assumes that all wires have the same stress-strain curve, greatly simplifying the calculations. The procedure for calculating cable strength is similar to that of the Brittle Wire Model; only an initial strain is assumed and varied rather than stress. The number of broken wires in each group is calculated using the cumulative Weibull distribution function of the ultimate strain. The stress in the cable is then determined using the wires’ assumed stress-strain curve. Like the Brittle Wire Model, this stress is then multiplied by the area of the remaining wires and estimates of the force in wires broken in other panels and redeveloped in the panel under consideration are added to determine the total force in the cable. The assumed strain is then varied until the maximum cable force is found. This is the estimated cable capacity. A spreadsheet can be used to automate this process (e.g. Microsoft Excel’s “Solver” add-on). The Modified Ramberg-Osgood Function, used to determine the stress in the wires at a given strain, was calculated as follows: ( ) 1/ 1 1 p pf CC pf Af E A B ε ε    − = +    +    (1) where: fp = wire stress E = wire modulus of elasticity ɛpf = wire strain A, B, and C = constants The stress-strain curves of a number of specimens (representing various corrosion stages) are then plotted along with the calculated curve. Linear regression is used to plot the average slope of the pre- yield and post-yield portions of the stress-strain curve. The constants are adjusted until the calculated curve matches the actual curve (as approximated by the linear regression plots).

49 Evaluation of Accuracy of Strength Estimation The process of developing an estimate of the strength based on cable inspection necessarily relies upon several assumptions. Only the wires along the wedge lines are inspected, and the results are used to estimate the condition of the rest of the wires inside the cable. Only the corrosion stage of the inspected wires is obtained and based on tests of other wires, a distribution of wire strength for the different corrosion stages is obtained and assumed to apply to all wires in the cable. In order to gauge the effectiveness of these assumptions, an evaluation was conducted by assuming that all relevant information was known about a single cable cross-section and then simulating an inspection and cable strength calculation to see how close that estimate would come to the strength of the assumed cross- section. For the evaluation, a sample cable cross-section consistent with the example presented in the illustrative example was assumed. The main cable comprises 6,080 high-strength steel galvanized wires, arranged in 46 rings. The corrosion stage of each wire in the cable was assumed, and a strength was assigned to each wire based on an assumed wire strength distribution. An inspection was then simulated along the eight wedge lines to determine the wire corrosion stage at the left- and right-hand sides. A total of 736 wires were thus examined along the wedge lines where 439 were at corrosion stages 1 and 2, 262 wires at corrosion stage 3, and 35 wires at corrosion stage 4. The cable cross-section map has known corrosion stages per wedge line and the position rings. To simplify the calculations, no broken or cracked wires were included in the cross-section. Thus, the comparative evaluation determines the cable strength for the two scenarios: 1. Assumed – corrosion stages and wire strengths are assumed for each wire in the cable cross-section individually. 2. Mapped – wires are distributed according to observed corrosion stages at wedge lines and the rings, per the methodology provided in the guidelines. Both the assumed and mapped scenario have the same corrosion stages for the wires along the wedge lines. The mapped scenario utilizes wedge inspection, and the geometrical distribution of wires within the rings to estimate the number of wires at each corrosion stage. The cable strength assessment contained in the NCHRP NCHRP Report 534 guidelines requires knowledge of wire corrosion distribution within a cross-section and the strength of individual wires. The strength of wires in each corrosion stage is treated as a random variable, and therefore there is a need to determine statistical parameters in terms of a mean and standard deviation of wire tensile strength. This is done by testing a sampling of wires in the various corrosion stages. The wire mean strength and its dispersion defined by the standard deviation allow simulation of wire strength at different corrosion stages. In this comparative analysis, the statistical parameters are taken from the test data provided in the illustrative example. Tensile test data was used to determine mean wire strength for corrosion stages 1, 2, 3, and 4, and corresponding standard deviations. To examine how variations in wire strength statistical parameters might affect the accuracy of the method, four additional cases with assigned statistical parameters were considered. Table 2 presents the statistical parameters for five cases in terms of the mean and standard deviation of wire strength presented in lbs. As mentioned above, Case 1 statistical parameters are consistent with the test data from an actual cable. Case 2 and 3 use similar wire strength mean proportions for each corrosion stage but with increased standard deviations. Cases 4 and 5 provide a significant dispersion in the mean value per corrosion stage. Although these types of distributions are not thought to be representative of any actual

50 cables, Cases 4 and 5 were considered to see how extremes of wire strength distribution may affect the accuracy of the strength estimates. Table 2. Statistical Parameters for Tensile Strength for Different Corrosion Stages and Selected Cases. Corrosion Stage Tensile Strength per Wire (lbs) Case 1 Case 2 Case 3 Case 4 Case 5 µ σ µ σ µ σ µ σ µ σ 1+2 6,796 305 4,700 600 8,600 1,900 6,800 600 9,150 1,900 3 6,827 272 4,800 550 8,400 1,750 6,200 550 8,350 1,750 4 6,441 532 4,400 750 8,200 2,100 5,800 750 7,135 2,100 A measure of the accuracy of the overall methodology is the comparison between the calculated strengths from the assumed and mapped scenarios. The cable strength was computed using the Simplified Strength Model from NCHRP NCHRP Report 534 for each of the five cases representing different statistical parameters of wires strength at different corrosion stages. Statistical parameters presented in Table 2 are used to simulate the wire strength at each corrosion stage. Both the assumed and mapped scenarios used the same distributions within each case. A comparison of the cable strengths between the assumed and mapped scenarios shows very good agreement. For Case 1 which uses the wire test data the difference between the two approaches in the simulation procedure is less than 1%. For the cases with increased standard deviation (Cases 2 and 3) the difference is no more than 3%, and for the extreme case with the mean value spread significantly per corrosion stage provides the difference in cable strength is no more than 5%. Although such a significant difference in the mean values is not expected for the uniform wires comprising a cable cross- section, the comparative analysis shows that the resulting difference in the cable strength is still relatively small. Based on the above evaluation, the inspection and wire mapping based on wedge line wire corrosion stage appears to be an accurate method of determining the relative proportions of wire corrosion stages in a cable as well as determining the cable strength. It is important to note that this evaluation looked at only one cross-section and did not include the variation in corrosion stage and strength along the length of a panel. Recommended Report Content Given the number and variety of inspections that are performed on suspension bridge cables, it is important to organize the results of each inspection and ensure adequate information is provided to document the cable condition and strength calculations. Over time, the reports form a historical record of the condition of the cable and help the bridge owner make informed decisions about maintenance schedules and budgets. This section provides minimum requirements for cable inspection reports. Maintenance Personnel Inspection A report shall be prepared for each periodic inspection performed by maintenance personnel. This report shall include at minimum: 1. date of inspection

51 2. weather and temperature 3. cable portion inspected (e.g., west main span, south anchorage, tower saddles and cable housings) 4. list of deficiencies, identified by panel number 5. one-page account of each deficiency with • verbal description (e.g., peeling paint, rust stains, broken wrapping) • color photograph • recommended action 6. list of recommended actions in order of priority A follow-up report shall be prepared for each action taken, with a description of the action and a photograph of the completed work. Biennial Inspection The basic report for a biennial inspection is described in specifications provided by the state departments of transportation; they are not repeated here. The report should also contain the following information about the cables and suspension system: 1. separate listings of the ratings applied to each component (e.g., wrapping, hand ropes, etc.) in each inspected panel (see Figures 2.2.2.1-1 and 2.2.3.1-3 of the proposed Guidelines) 2. photographs of deficiencies 3. reasons for ratings lower than 5 (on a scale of 1 to 7) 4. recommendations for action 5. reasons for recommending an internal inspection, if applicable Internal Inspection The report for an internal inspection shall include all of the following: • 1. executive summary providing a brief synopsis of the findings of the inspection that incorporates • number of locations opened for inspection • general description of conditions found (e.g., severe corrosion with 15 broken wires) • strength of each panel investigated • safety factor of each panel investigated • safety factor using the panel with lowest strength and maximum cable tension (usually adjacent to the tower) • recommendations for remedial action • recommendation for date of next inspection 2. table of contents 3. summary addressing executive summary items in greater detail 4. findings from preliminary cable walk and reasons for selecting investigated panels 5. plan and elevation of cables showing location of panels investigated 6. description and photographs of the means of access to the cable 7. detailed descriptions of each panel opened; cable cross-sections showing wedge locations, distribution of stages of corrosion and location of broken wires 8. summary of laboratory test results; cable cross- sections showing locations of sample wires

52 9. verbal description of method used to calculate cable strength; table of calculated strengths 10. table of cable tensions due to dead load, live load and temperature; table of cable safety factors 11. investigator’s estimate of the accuracy of estimated cable strength 12. conclusions • discussion of cable strengths, safety factors and possible errors • discussion of probable causes of deterioration 13. recommendations • plan for continued operation of the bridge if the safety factor is low • general plan for maintenance and repairs • specific plan for time of next inspection and number of panels to be inspected (The exact panels should be selected during the preparatory period for the next inspection, unless follow-up inspections of specific panels are recommended.) 14. appendices • laboratory reports for: o Wire properties from tests; means and standard devications of corrosion groups o Weight or Zinc Coating Test and Preece Test o Chemical testing of metal and corrosion products o Metallurgical examinations, including photographs • Sample strength calculations • Selected photographs showing condition of cable exterior (from the cable walk) and cable interior (from wedging) • Selected photographs of inspection and rewrapping operations